ANALYTICAL CHEMISTRY, VOL. 51, NO. 9, AUGUST 1979
formed after step 3 was unable to show the presence of water, which indicates a content below 100 ppm. The quality of the purified MeCN is further demonstrated in Tables I1 and 111, where its electrochemical and spectroscopic properties are compared to the practical grade starting material and to an expensive (The price ratio between a commercial UV grade and a practical grade MeCN is normally a t least 30.), commercially available UV quality PdeCN (Fluka).
Table 111. Transmittance (T)of MeCN as Function of Wavelength ( h )
h,
nm
240 230
practical grade% T
Fluka UV, % T
57 50
100 100
5 1
96 84 75 68
220 210 205
-
200
-
195 190 189 188 187
-
-
43 10 10
14 28
1595
purified as described,
%T 100
98 89 75 72 65 35
ACKNOWLEDGMENT I t is a pleasure to acknowledge the assistance of B. Svensmark Jensen in running the electrochemical measurements.
12
12 15 32
LITERATURE C I T E D
allylalcohol, amines, and benzene); and (3) removal of water by passing through activated alumina. The overall yield of purified MeCN is approximately 70%. After the two distillations, the amounts of acrylonitrile, allylalcohol, and benzene are below our detection limits, see Table I. As we intentionally added n-octanol in step 1,we monitored the content of that compound too, and show the results in Table I also. A Karl Fischer determination per-
(1) Andersen, J. R., Engler, E. M., Bechgaard, K., Ann. N . Y . Acad. Sci. 1970, 313, 293. (2) Weissberger, A., Proskauer, E., Riddick, J., Toops, E., Eds. "Technique of Organic Chemistry" Vol. VII, 2nd ed.; Interscience: New York, 1955. ( 3 ) Coetzee, J. F., Cunningham, G. P., McGuire. D. K., Padmanabhan, G. R. Anal. Chem. 1962 34, 1139. (4) O'Donnell, J. F., Ayres, J. T., Mann, C. K . Anal. Chem. 1965, 37, 1161. (5) Forcier, G. A,, Olver, J. W. Anal. Chem. 1965, 3 7 , 1447.
RECEIVED for review January 15, 1979. Accepted April 23, 1979.
Estimation of Water Content by Kinetic Method in Karl Fischer Titration W. T. Yap," A. L. Cummings, S. A. Margolis, and Robert Schaffer Center for Analytical Chemistry, National Bureau of Standards, Washington, D.C. 20234
Determinations of the water content of solids by the Karl Fischer method are rather common. The principles and applications of various Karl Fischer titration systems can be found in the literature (1-3). Using various types of automated apparatus, not only the end point but also the time course of the titration, Le., the titration curve, is obtained. The Karl Fischer reagent delivered from the automatic buret is related to the rate at which the sample dissolves, and it is recorded as a function of time. With slow rates of dissolution, it may take many hours to reach the end point, with consequent enlargement of sources of error. By analysis of only part of the experimental titration curve before the end point, it is possible to calculate the water content of the sample and some of the kinetic parameters. T h e T i t r a t i o n Curve. The rate of release of water from the solids into the solution is assumed to be proportional to the rate of dissolution of the solid. The latter rate is taken to be proportional to the total surface area, S, of the solids and to the solution saturation deficiency (c, - c) (4,i.e. d W / d t = -kS (c, - C)
(1)
where c is the concentration of the solute, c, is the solubility of the solute in the given solvent, W is the mass of the solid a t time t , and k is the rate constant. If we let r denote an average linear dimension of the solids, V the volume of the solution, and subscript 0 the values a t t = 0, then
and
m/v
c = (W, -
WO
= - (1 - x3)
(4)
V
where x = r/ro. Substituting Equations 2, 3, and 4 into Equation 1 gives, after simplifying,
d x / d t = -A(1
-
b(l - x3))
(5)
where A = kS,c,/3 W, and b = W,/ Vc,. Integrating Equation 5, using the boundary condition: x = 1 a t t = 0, gives (5) 3(1 - b ) A U
t = In
+ a ) (x2 ax + U2)1'* + (x + a ) ( l a + a2)1/2 fi (arctan E lh arctan (1
-
-
-
l h xx )
2a
-
=F(b;x) (6) where a = ((1- b)/b)'I3. At time t , the total amount of water which had gone into the solution is given by g=
w, (1
- X3)f
(7)
where f is the mass fraction of water originally in the sample. Equations 6 and 7 are a set of parametric equations relating g and t , with x as the parameter. Plots of g vs. t would give the titration curves for various given experimental conditions. Estimation of t h e Fraction of Water in Solids. F ( b ; x ) is a family of functions of x , having as parameter the degree of saturation b; Le., b , as defined above, is the ratio of the
This article not subject to U.S. Copyright. Published 1979 by the American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 51, NO. 9, AUGUST 1979 I
"1
I I;/ 1
10b=8
I
I
6
4 2
I
I
I
I
I
I
I
I
1
I
; ;/ l -
-
i
-
j/ 0.
-I
I
I
I
I
I
I
In both series of experiments mentioned above, Le., the titrations of magnesium gluconate and of sucrose, the precision in the estimation of the mass fraction of water in the samples is about 10%. And the average values of the mass fraction of water estimated by the kinetic method agree, respectively, with those estimated from the conventional end-point determinations of the Karl Fischer titration to well within 10%.
LITERATURE CITED (1) Cedergren, A. Talanta 1974, 27, 553-563. (2) Beaseley, T. H.,3 . ; Ziegler, H. W.; Charles, R. L.; King, P. Anal. Chem. 1972, 44, 1833-1840. (3) Verholf, V. C.; Barendrecht, E. J , Hectroanal. Chem. Interfacial Nectrochem. 1976, 7 7 , 305-315. (4) Moelwyn-Hughes, E. A. "Physical Chemistry", 2nd ed.,;Macmillian: New York, 1961; Chapter 23. (5) Gradshteyn, I. S.; Ryzhik. I. M. "Table of Integrals, Series and Products"; Academic Press: New York, 1965; p 63.
RECEIVED for review April 9, 1979. Accepted May 15, 1979.
